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Sample means and sample variances

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Reference no: EM132096728

Problem: Let X1, X2, X3, X4 be iid random variables each one with probability N(10, 4σ).

Let Y1, Y2, Y3 be iid random variables each one with probability N(5, 3σ).

The two samples are independent. Also, let ???X?¯???? , ???Y?¯????, S2X, S2Y be the corresponding sample means and sample variances of the two samples.

Answer the following questions:

a. What is the distribution of ???X?¯??-?Y?¯???? ?

b. What is the distribution of ??16σ?2????3S?X?2????+?9σ?2????2S?Y?2????? ?

For (a) I got that ???X?¯??-?Y?¯???? ~ N[5, ??σ√?7????? ].

Reference no: EM132096728

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